So. A few things.
The Doctor lies.
He whispered in her ear to look in his eye, but then proclaimed that he told her his name.
The Doctor lies.
River whispered in his ear and he then proclaimed that she told him his name.
It seems unlikely. But it's Moffat. Perhaps she told him to look into her eye. Perhaps it was another robot like the Tessalecta, with the 11th waiting inside with the TARDIS. Just a thought.
Another thing. I think the voice singing the "Tick tock, goes the clock, even for The Doctor." and all that. I think that was young Melody Pond. The Melody Pond that called the president.
And one last thing. The time line. Original time line, The Doctor is killed by the astronaut/River. Amy, Rory and River then go to what I think was a restaurant and find the younger Doctor. They then set out on an adventure that leads them back to The God Complex, The Doctor leaving them, and then his death. BUT it showed Amy, Rory, and River drinking together. Amy was still shell shocked and in disbelief that she just saw him die. River than reveals that he's alive. But when would that fit in? Did the time line change? I mean, the fixed point of his "death" remains, but the details around it can change. Do we have altered time line going on? or?